// -------------------------------------------------------------------------
public void test_priceSensitivity() {
PointSensitivities point =
OPTION_PRICER.priceSensitivityStickyStrike(
FUTURE_OPTION_PRODUCT, RATE_PROVIDER, VOL_PROVIDER);
CurveCurrencyParameterSensitivities computed = RATE_PROVIDER.curveParameterSensitivity(point);
CurveCurrencyParameterSensitivities expected =
FD_CAL.sensitivity(
RATE_PROVIDER,
(p) ->
CurrencyAmount.of(
EUR, OPTION_PRICER.price(FUTURE_OPTION_PRODUCT, (p), VOL_PROVIDER)));
double futurePrice = FUTURE_PRICER.price(FUTURE_OPTION_PRODUCT.getUnderlying(), RATE_PROVIDER);
double strike = FUTURE_OPTION_PRODUCT.getStrikePrice();
double expiryTime =
ACT_365F.relativeYearFraction(VALUATION_DATE, FUTURE_OPTION_PRODUCT.getExpiryDate());
double logMoneyness = Math.log(strike / futurePrice);
double logMoneynessUp = Math.log(strike / (futurePrice + EPS));
double logMoneynessDw = Math.log(strike / (futurePrice - EPS));
double vol = SURFACE.zValue(expiryTime, logMoneyness);
double volUp = SURFACE.zValue(expiryTime, logMoneynessUp);
double volDw = SURFACE.zValue(expiryTime, logMoneynessDw);
double volSensi = 0.5 * (volUp - volDw) / EPS;
double vega = BlackFormulaRepository.vega(futurePrice, strike, expiryTime, vol);
CurveCurrencyParameterSensitivities sensiVol =
RATE_PROVIDER
.curveParameterSensitivity(
FUTURE_PRICER.priceSensitivity(
FUTURE_OPTION_PRODUCT.getUnderlying(), RATE_PROVIDER))
.multipliedBy(-vega * volSensi);
expected = expected.combinedWith(sensiVol);
assertTrue(computed.equalWithTolerance(expected, 30d * EPS));
}
/** Calculate the true SABR delta and gamma and compare with that found by finite difference */
@Test(enabled = false)
public void testGreeks() {
double eps = 1e-3;
double f = 1.2;
double k = 1.4;
double t = 5.0;
double alpha = 0.3;
double beta = 0.6;
double rho = -0.4;
double nu = 0.4;
SabrFormulaData sabrData = SabrFormulaData.of(alpha, beta, rho, nu);
ValueDerivatives adj = FUNCTION.getVolatilityAdjoint(f, k, t, sabrData);
double bsDelta = BlackFormulaRepository.delta(f, k, t, adj.getValue(), true);
double bsVega = BlackFormulaRepository.vega(f, k, t, adj.getValue());
double volForwardSense = adj.getDerivative(1);
double delta = bsDelta + bsVega * volForwardSense;
SabrFormulaData data = SabrFormulaData.of(alpha, beta, rho, nu);
double volUp = FUNCTION.getVolatility(f + eps, k, t, data);
double volDown = FUNCTION.getVolatility(f - eps, k, t, data);
double priceUp = BlackFormulaRepository.price(f + eps, k, t, volUp, true);
double price = BlackFormulaRepository.price(f, k, t, adj.getValue(), true);
double priceDown = BlackFormulaRepository.price(f - eps, k, t, volDown, true);
double fdDelta = (priceUp - priceDown) / 2 / eps;
assertEquals(fdDelta, delta, 1e-6);
double bsVanna = BlackFormulaRepository.vanna(f, k, t, adj.getValue());
double bsGamma = BlackFormulaRepository.gamma(f, k, t, adj.getValue());
double[] volD1 = new double[5];
double[][] volD2 = new double[2][2];
FUNCTION.getVolatilityAdjoint2(f, k, t, sabrData, volD1, volD2);
double d2Sigmad2Fwd = volD2[0][0];
double gamma = bsGamma + 2 * bsVanna * adj.getDerivative(1) + bsVega * d2Sigmad2Fwd;
double fdGamma = (priceUp + priceDown - 2 * price) / eps / eps;
double d2Sigmad2FwdFD = (volUp + volDown - 2 * adj.getValue()) / eps / eps;
assertEquals(d2Sigmad2FwdFD, d2Sigmad2Fwd, 1e-4);
assertEquals(fdGamma, gamma, 1e-2);
}